Question: Solve for $x$ : $3\sqrt{x} + 1 = 10\sqrt{x} + 7$
Subtract $3\sqrt{x}$ from both sides: $(3\sqrt{x} + 1) - 3\sqrt{x} = (10\sqrt{x} + 7) - 3\sqrt{x}$ $1 = 7\sqrt{x} + 7$ Subtract $7$ from both sides: $1 - 7 = (7\sqrt{x} + 7) - 7$ $-6 = 7\sqrt{x}$ Divide both sides by $7$ $\frac{-6}{7} = \frac{7\sqrt{x}}{7}$ Simplify. $-\dfrac{6}{7} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.